Date: March 2015

Duration: 2h

In the following figure seg AB ⊥ seg BC, seg DC ⊥ seg BC. If AB = 2 and DC = 3, find `(A(triangleABC))/(A(triangleDCB))`

Chapter: [1] Similarity

Find the slope and y-intercept of the line y = -2x + 3.

Chapter: [4] Co-ordinate Geometry

In the following figure, in ΔABC, BC = 1, AC = 2, ∠B = 90°. Find the value of sin θ.

Chapter: [6] Trigonometry

Find the diagonal of a square whose side is 10 cm.

Chapter: [7] Mensuration

The volume of a cube is 1000 cm^{3}. Find the side of a cube.

Chapter: [7] Mensuration

If two circles with radii 5 cm and 3 cm respectively touch internally, find the distance between their centres.

Chapter: [3] Circle

If sin θ =7/25, where θ is an acute angle, find the value of cos θ.

Chapter: [6] Trigonometry

Draw ∠ABC of measure 120° and bisect it.

Chapter: [5] Geometric Constructions

Find the slope of the line passing through the points M(4,0) and N(-2,-3).

Chapter: [4] Co-ordinate Geometry

Find the area of the sector whose arc length and radius are 14 cm and 6 cm respectively.

Chapter: [7] Mensuration

In the following figure, in Δ PQR, seg RS is the bisector of ∠PRQ.

PS = 11, SQ = 12, PR = 22. Find QR.

Chapter: [1] Similarity

In the following figure, if m(arc DXE) = 120° and m(arc AYC) = 60°. Find ∠DBE.

Chapter: [7] Mensuration

In the following figure, Q is the centre of a circle and PM, PN are tangent segments to the circle. If ∠MPN = 60°, find ∠MQN.

Chapter: [3] Circle

Draw the tangents to the circle from the point L with radius 3 cm. Point ‘L’ is at a distance 8 cm from the centre ‘M’.

Chapter: [5] Geometric Constructions

The ratio of the areas of two triangles with the common base is 4 : 3. Height of the larger triangle is 2 cm, then find the corresponding height of the smaller triangle.

Chapter: [1] Similarity

Two buildings are in front of each other on either side of a road of width 10 metres. From the top of the first building which is 20 metres high, the angle of elevation to the top of the second is 45°. What is the height of the second building?

Chapter: [6] Trigonometry

Find the volume and surface area of a sphere of radius 8.4 cm.

`(pi=22/7)`

Chapter: [7] Mensuration

Prove that ‘the opposite angles of a cyclic quadrilateral are supplementary’.

Chapter: [3] Circle

Prove that sin^{6}θ + cos^{6}θ = 1 – 3 sin^{2}θ. cos^{2}θ.

Chapter: [6] Trigonometry

A test tube has diameter 20 mm and height is 15 cm. The lower portion is a hemisphere. Find the capacity of the test tube. (π = 3.14)

Chapter: [7] Mensuration

Prove that the angle bisector of a triangle divides the side opposite to the angle in the ratio of the remaining sides.

Chapter: [1] Similarity

Write down the equation of a line whose slope is 3/2 and which passes through point P, where P divides the line segment AB joining A(-2, 6) and B(3, -4) in the ratio 2 : 3.

Chapter: [5] Geometric Constructions

ΔRST ~ ΔUAY, In ΔRST, RS = 6 cm, ∠S = 50°, ST = 7.5 cm. The corresponding sides of ΔRST and ΔUAY are in the ratio 5 : 4. Construct ΔUAY.

Chapter: [5] Geometric Constructions

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